How do you find the complex conjugate of [4 - sqrt(-3)]/ 2?

Feb 5, 2016

The complex conjugate of $\frac{4 - \sqrt{- 3}}{2}$
is
$2 + \frac{\sqrt{3}}{2} i$

Explanation:

First note
$\textcolor{w h i t e}{\text{XXX}} \frac{4 - \sqrt{- 3}}{2} = 2 - \frac{\sqrt{3}}{2} i$

The complex conjugate of a complex number is
a number with
$\textcolor{w h i t e}{\text{XXX")color(red)("the real component equal to the real component of the original number}}$
and
$\textcolor{w h i t e}{\text{XXX")color(blue)("the complex component equal in magnitude but opposite in sign.}}$

So the complex conjugate of $\textcolor{red}{2} \textcolor{b l u e}{- \frac{\sqrt{3}}{2}} i$
is $\textcolor{red}{2} \textcolor{b l u e}{+ \frac{\sqrt{3}}{2}} i$